BCD Converter (8421)
Convert between decimal numbers and Binary Coded Decimal. Each decimal digit is encoded separately using 4 bits.
What is Binary Coded Decimal (BCD)?
Binary Coded Decimal is a numeric representation where each decimal digit (0 through 9) is stored as its own 4-bit binary value. Instead of converting the entire number to pure binary, BCD handles each decimal digit one by one.
For example, the decimal number 59 is represented in BCD as:
5 → 01019 → 1001- BCD result:
0101 1001
This differs from pure binary, where 59 would be 111011. BCD is less space-efficient, but much easier for decimal displays and financial-style calculations.
How to use this BCD calculator
Decimal to BCD
- Enter a non-negative decimal number in the Decimal Input field.
- Click Convert Decimal → BCD.
- The calculator outputs 4-bit groups for each digit.
BCD to Decimal
- Enter bits in the BCD Input field (with or without spaces).
- Click Convert BCD → Decimal.
- Only valid BCD nibbles (
0000to1001) are accepted.
BCD digit mapping table (8421 code)
| Decimal Digit | BCD (4-bit) |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
Why engineers still use BCD
Even though binary is more compact, BCD remains useful in many systems:
- Digital clocks and counters: BCD makes 7-segment display driving straightforward.
- Financial and accounting hardware: Decimal precision can be managed cleanly without binary floating-point surprises.
- Embedded systems: Legacy chips and interfaces often rely on BCD registers.
- Human-readable values: Conversion between display digits and stored data is simple.
Common mistakes and validation rules
1) Treating BCD like normal binary
If you decode BCD as plain binary, your result will be wrong. In BCD, every 4-bit block is a separate decimal digit.
2) Using invalid nibbles
Values 1010 through 1111 are invalid in standard 8421 BCD. This calculator flags them immediately.
3) Forgetting 4-bit alignment
BCD input must contain a number of bits divisible by 4. If not, the groups are incomplete and cannot be decoded safely.
Quick examples
- Decimal 407 → BCD
0100 0000 0111 - BCD 0011 0001 → Decimal
31 - BCD 1001 1001 → Decimal
99
Final note
This binary coded decimal calculator is intended for learners, electronics hobbyists, and engineers who need quick, accurate conversion. Use it for homework checks, embedded debugging, digital logic practice, or data format verification.